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In the asymptotic setting, a family of deterministic polynomial time computable functions : {,} {,} for some polynomial p, is a pseudorandom number generator (PRNG, or PRG in some references), if it stretches the length of its input (() > for any k), and if its output is computationally indistinguishable from true randomness, i.e. for any probabilistic polynomial time algorithm A, which ...
It can be shown that if is a pseudo-random number generator for the uniform distribution on (,) and if is the CDF of some given probability distribution , then is a pseudo-random number generator for , where : (,) is the percentile of , i.e. ():= {: ()}. Intuitively, an arbitrary distribution can be simulated from a simulation of the standard ...
If a full derandomization is desired, a completely deterministic simulation proceeds by replacing the random input to the randomized algorithm with the pseudorandom string produced by the pseudorandom generator. The simulation does this for all possible seeds and averages the output of the various runs of the randomized algorithm in a suitable way.
With a 128-bit block cipher, this would produce statistically identifiable deviations from randomness; for instance, generating 2 64 genuinely random 128-bit blocks would produce on average about one pair of identical blocks, but there are no repeated blocks at all among the first 2 128 produced by a 128-bit cipher in counter mode.
These approaches combine a pseudo-random number generator (often in the form of a block or stream cipher) with an external source of randomness (e.g., mouse movements, delay between keyboard presses etc.). /dev/random – Unix-like systems; CryptGenRandom – Microsoft Windows; Fortuna
A counterpart to /dev/random is /dev/urandom ("unlimited" [8] /non-blocking random source [7]) which reuses the internal pool to produce more pseudo-random bits. This means that the call will not block, but the output may contain less entropy than the corresponding read from /dev/random .
Lavarand, also known as the Wall of Entropy, is a hardware random number generator designed by Silicon Graphics that worked by taking pictures of the patterns made by the floating material in lava lamps, extracting random data from the pictures, and using the result to seed a pseudorandom number generator.
In 1992, further results were published, [11] implementing the ACORN Pseudo-Random Number Generator in exact integer arithmetic which ensures reproducibility across different platforms and languages, and stating that for arbitrary real-precision arithmetic it is possible to prove convergence of the ACORN sequence to k-distributed as the ...